Quantum spiral spin-tensor magnetism

The characterization of quantum magnetism in a large spin ($\geq 1$) system naturally involves both spin-vectors and -tensors. While certain types of spin-vector (e.g., ferromagnetic, spiral) and spin-tensor (e.g., nematic in frustrated lattices) orders have been investigated separately, the coexistence and correlation between them have not been well explored. Here we propose a novel quantum spiral spin-tensor order on a spin-1 Heisenberg chain subject to a spiral spin-tensor Zeeman field, which can be experimentally realized using a Raman-dressed cold atom optical lattice. We develop a method to fully characterize quantum phases of such spiral tensor magnetism with the coexistence of spin-vector and spin-tensor orders as well as their correlations using eight geometric parameters. Our method provides a powerful tool for characterizing spin-1 quantum magnetism and opens an avenue for exploring novel magnetic orders and spin-tensor electronics/atomtronics in large-spin systems.